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The role of the Seiberg-Witten field redefinition in renormalization of noncommutative chiral electrodynamics

It has been conjectured in the literature that renormalizability of the $θ$-expanded noncommutative gauge theories improves when one takes into account full nonuniqueness of the Seiberg-Witten expansion, which relates noncommutative (`high-energy') with commutative (`low-energy') fields. In order to check this conjecture we analyze renormalizability of the noncommutative chiral electrodynamics: we quantize the action which contains all possible terms implied by the SW map. After renormalization we arrive at a different theory in which the relation between the coupling constants is changed. This means that the $θ$-expanded chiral electrodynamics is not renormalizable: when fermions are included, the SW expansion is not preserved in quantization.